Suppose ordinarily half your class would get an A and half would get a B, with A students having a 25% chance of getting an A and B students having a 25% of getting an A. It costs $100 to persuade the instructor to raise a B grade to an A. A student is willing to pay $40 to insure she will get her usual grade and $70 to insure she will get a higher grade than usual.
a. If all students buy insurance that guarantees them an A, what is the zero profit price for an insurance company that offers A insurance.
b. Will grade insurance be sold in equilibrium?
c. Who would buy insurance and at what price if the insurance companies could tell what type of student each student is?
d. Is either the result in (b) or (c) efficient?

What will be an ideal response?


a. 0.25(0.5)100+0.75(0.5)100=$50.

b. A students will pay a maximum of $40 to insure their usual grade -- so they are not willing to pay the zero profit price that assumes everyone buys insurance. If only B students buy the insurance, the zero-profit price is 0.75(100)=$75. But B-students are only willing to pay $70 for A-insurance. So no insurance will be sold in equilibrium.

c. A students would be offered A-insurance at a price of $25 -- and would buy it at that price. B students would be offered A-insurance at the price of $75 and would not buy it.

d. The result in (c) is efficient -- A students have an expected cost of $25 and an expected benefit of $40 -- so surplus is created when insurance is sold to them at $25. B students have an expected cost of $75 but an expected benefit of only $70 -- so it would be inefficient for them to be insured.

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